The primary webometric method for estimating the online impact of an organization is to count links to its website. Link counts have been available from commercial search engines for over a decade but this was set to end by early 2012 and so a replacement is needed. This article compares link counts to two alternative methods: URL citations and organization title mentions. New variations of these methods are also introduced. The three methods are compared against each other using Yahoo!. Two of the three methods (URL citations and organization title mentions) are also compared against each other using Bing. Evidence from a case study of 131 UK universities and 49 US Library and Information Science (LIS) departments suggests that Bing's Hit Count Estimates (HCEs) for popular title searches are not useful for webometric research but that Yahoo!'s HCEs for all three types of search and Bing's URL citation HCEs seem to be consistent. For exact URL counts the results of all three methods in Yahoo! and both methods in Bing are also consistent. Four types of accuracy factors are also introduced and defined: search engine coverage, search engine retrieval variation, search engine retrieval anomalies, and query polysemy.